Do not want to redirect the same page after submit in MVC

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Ajax

MVC

jQuery

Currently, partial is getting submitted using AJAX after submit button click in main view. But I do not want the same partial to redirect after submission. How can I get rid off this. I am new to MVC so do not have much ideas. I have simply returned the partials in [HttpPost] ActionResult. I think, this is not correct way of doing this. Please guide me.

What I have tried:

Controller

[HttpPost]
public ActionResult Home(ClsAA clsAA)
{     
    ModelState.Clear();  
    if (Id == "Z01")
    {
        return PartialView("~/Views/Home/_P.cshtml", clsAA);
    }
    else if (Id == "P02")
    {
        return PartialView("~/Views/Home/_I.cshtml", clsAA);
    }
    return PartialView();                                        
}

Main View

<table>
    <tr>
        <th>@Html.DisplayNameFor(m => m.ProductName)</th>
        <th>@Html.DisplayNameFor(m => m.ProductDetail)</th>
        <th>@Html.DisplayNameFor(m => m.ProductCost)</th>     
    </tr>
    @foreach (var item in Model)
    {
        <tr>
            <td>@Html.DisplayFor(modelItem => item.ProductName)</td>
            <td >@Html.DisplayFor(modelItem => item.ProductDetail)</td>
            <td>@Html.DisplayFor(modelItem => item.ProductCost)</td>
            <td><input class="search btn-default" type="button" value="Select" data-assigned="@item.ProductCode"/></td>
        </tr>
    }
</table>
<div id="MyReports">
    @using (Html.BeginForm("Home", "Home", FormMethod.Post, new { id = "myform" }))
    {
        <div id="mypartial"></div>              
        <button type="submit" id="submit">Run</button>              
    }
</div>

This is how Partial loads

$('.search').click(function () {
    var id = $(this).data('assigned');
    var route = '@Url.Action("PartialView", "Home")?id=' + id;        
    $('#mypartial').load(route)
});

Partial View

<div class="PContainer">
    <label>
        @Html.RadioButtonFor(m => m.HDT, "H", new { @checked = "checked" })H
    </label>
    <label>
        @Html.RadioButtonFor(m => m.HDT, "T")T
    </label>
</div>
<div class="P">
    <div id="H" class="PHT">
        @Html.TextBoxFor(m => m.txtH)  
    </div>
    <div id="T" class="PHT">
        @Html.TextBoxFor(m => m.txtT)               
    </div>
</div>

Scripts for submit

$(document).ready(function () {
    var url = '@Url.Action("Home")';
    $('#myform').submit(function () {
        if (!$(this).valid()) {
            return;
        }
        $.post(url, $(this).serialize(), function (response) {
            debugger;
            $('#mypartial').html(response);
            $("#myModal").modal('show');     
        });
        return false;
    })
});